208 
MINUTES OF PROCEEDINGS OF 
In the above figure let the abscissae represent the strains and the 
ordinates the total extensions of a bar of metal (experimentally deter¬ 
mined) corresponding to the strains. 
If the bar be subject to a constantly increasing strain the elongation 
is first constant in proportion to the strain,* increasing after a certain 
point in a higher proportion. This point, represented in the diagram 
by the extension of HJ and measured by the statical strain correspond¬ 
ing to the abscissa AJ, is termed the “ limit of elasticity.”f 
After this point is reached the extensions increase in a higher 
proportion for every increment of strain and the line joining the 
ordinates becomes a curved line, as shown in the figure at D, the total 
extension of the bar at that point being represented by BD and the 
breaking strain by the abscissa AT) which is the measure of the “ limit 
of fracture.” J We have then, as will be seen by the fig., three exten¬ 
sions of the bar, the “ total,” “ elastic,” and “permanent,” the former 
being in all cases the sum of the two latter, while, until the “ limit of 
elasticity ” is reached, the total extension is synonymous with the 
“elastic” extension—(strictly not quite so but very nearly). 
The curve (a straight line as far as H) AB represents the total 
extensions, and the straight line AG the elastic extensions of the bar, 
while the total mechanical force required to produce rupture corres¬ 
ponds to the area ABB. 
Similarly the mechanical force necessary to produce a total extension 
EF corresponds to the area AFE. 
If we remove the pressure represented by AF, after the bar has been 
elongated by EF, and then re-impose it, the greatest extension of the 
bar will not exceed FG\\; and if we once more remove the strain the 
bar will revert to its former length, i.e., its original length + EG : 
Here, of the total work done on the bar, represented bv the area 
AFE, that portion corresponding to the area HEG has been absorbed 
by it and applied to the re-arrangement of its molecules, being the 
measure of the loss sustained in the total tenacity of the bar. Its 
breaking strain may however be increased, and we see that its elasticity 
is so, for any ductile metal increases (within certain limits) in elasticity 
and ultimate strength (as represented by the breaking strain), though 
not in absolute strength, (as shown by total work or mechanical force 
required to produce rupture) when subjected to drawing, hammering, 
or rolling. In fact, a material strained beyond its limit of elasticity 
will exhibit the same characteristics as an original harder metal. 
To return, however, to the case in the figure:—Suppose we now 
# This extension increases very slightly in proportion of the duration of the strain. 
f By some, as before mentioned, termed the “ limit of cohesion.” 
X This limit of fracture is often said to be a measure of the “ tenacity” or “ tensile 
strength” of a metal, but is in reality only a measure of the “ultimate” tenacity, or 
ultimate “ tensile strength.” i.e. the breaking strain, and does not represent the total 
strength of a given metal to withstand a strain, or in other words, the total mechanical 
force required to produce rupture .—Vide Mallet’s explanation, “Construction of Artillery,” 
p. 73. 
[J This, however, according to Mallet, p. 57, will not always be the case if we reimpose 
the weight for any time. With wrought-iron, for instance, should the strain exceed 
one-fourth the rupturing strain, the extension will slowly increase with time. 
